1. Technical Field
The present disclosure is related generally to control systems for industrial processes, and more particularly, to a modified proportional integral derivative (PID) controller that drives electro-pneumatic valve actuators to regulate a fluid flow control process.
2. Related Art
Many industrial processes involve the movement of fluid such as gas, steam, water, and chemical compounds. The flow of the fluid is regulated by a control valve that has a passageway that is selectively opened and closed with a movable obstruction or valve element connected to a stem. An actuator, in turn, is connected to the stem, and provides the motive force to open and close the valve element. Pneumatic, hydraulic, electrical, or mechanical energy is converted by the actuator to linear or rotational motion, depending on the configuration of the control valve. Pneumatic systems are typically utilized for valve actuators due to several distinct advantages, but primarily for the quicker and more precise degree of control.
A conventional pneumatic actuator is comprised of a piston sealed within a cylinder, and the piston including a connecting rod that is mechanically coupled to the valve element. Compressed air is forced into and out of the cylinder to move the connecting rod, which is mechanically coupled to the stem of the control valve.
Precise and accurate control of the valve actuator, and hence the valve element, can be achieved with a positioner device coupled thereto. An electrical control circuit provides a variable current signal to the positioner device that proportionally corresponds to particular states of the actuator and hence a particular position of the control valve. The electrical control circuit and the electrical current signals generated thereby may be part of a broader process managed by a distributed control system. Generally, the electrical current varies between 4 milliamps (mA) and 20 mA according to industry-wide standards; at 4 mA the valve positioner may fully open the valve element, while at 20 mA, the valve positioner may fully close the valve element.
The desired state of the actuator represented by the electrical current, which is the desired position of the control valve, is referred to as the set point. For pneumatic valve actuators, the related positioner device includes a spool that rotates or slides axially in a housing to port compressed air from a pressure line to the valve actuator, with the movement of the spool being governed by the electrical signal. The positioner device compares the set point to the current position of the actuator and determines if there is a difference or error. Additional adjustments to the position of the spool are made to adjust the flow of compressed air to the valve actuator so that the margin between the set point and the process variable, i.e., the error, is reduced. The measured position feedback of the actuator may also be referred to as the process variable, while the position of the spool is referred to as the manipulated variable.
The manipulated variable output is a function of the particular feedback control loop implemented by the positioner device. Depending on the specifics of the feedback control loop, response time, overshoot, and damping ratios can differ. Response time refers to the speed at which positioner device responds to a change in the set point, overshoot refers to the extent to which the manipulated variable initially exceeds a new set point, and damping ratio refers to the rate at which the manipulated variable reaches a steady state after a new set point.
One commonly implemented feedback control loop function is proportional-integral-derivative (PID) control. Standard PID control is well known in the art, and is understood to be suitable for applications where accurate maintenance of the process variable is important, such as fluid flow control valves in an industrial process. PID controllers are typically implemented digitally on dedicated microprocessors. The manipulated variable output, or corrective gain, is a sum of proportional integral, and derivative terms that are functions of the magnitude of error. Specifically, the proportional term is a product of a proportional gain KP and the error e at a particular instant in time t, and represents a reaction to current error. The proportional term is commonly notated as:
KPe(t) in the analog domain, or KPen in the digital domain.
The integral term is a product of the sum of past instantaneous errors e over time t and an integral gain KI. The integral term is used to correct steady state error, and is commonly notated as:
            KI      ⁢                        ∫          0          t                ⁢                              e            ⁡                          (              τ              )                                ⁢                                          ⁢                      ⅆ            t                    ⁢                                          ⁢          in          ⁢                                          ⁢          the          ⁢                                          ⁢          analog          ⁢                                          ⁢          domain                      ,    or        KI    ⁢                  ∑                  K          =          0                n            ⁢                        (                                    e              K                        +                          e                              K                -                1                                              )                ⁢                                  ⁢        in        ⁢                                  ⁢        the        ⁢                                  ⁢        digital        ⁢                                  ⁢                  domain          .                    
The derivative term is a product of the rate of change of error e over time t and a derivative gain KD. The derivative term is used to reduce the magnitude of overshoot, and hence oscillation, caused by the integral term. It also serves to reduce the time needed to reach a steady state, and increase stability. It is commonly notated as:
            KD      ⁢                        ⅆ                      e            ⁡                          (              t              )                                                ⅆ          t                    ⁢                          ⁢      in      ⁢                          ⁢      the      ⁢                          ⁢      analog      ⁢                          ⁢      domain        ,    or              KD      ⁡              (                              e            n                    -                      e                          n              -              1                                      )              ⁢                  ⁢    in    ⁢                  ⁢    the    ⁢                  ⁢    digital    ⁢                  ⁢          domain      .      
Conventional PID controllers have a number of deficiencies, particularly when used in connection with high dynamic systems such as valve positioners with high flow rate spools and high-speed actuator devices. Despite substantial improvements in microprocessors that have increased calculation speeds of the PID mathematical calculations, there remains slow oscillations around the set point resulting from the integral term, vibration/noise associated with the derivative term, and so forth. Accordingly, there is a need in the art for an improved proportional integral derivative controller.